Suppose there are two types of workers, k = G, B, differentiated by their productivity levels. Type G workers have productivity k = 2 and type B workers have productivity k= 1. The cost of achieving a given level of education is higher for type B than type G е workers. The cost function of a type k to achieve education level e is c(e; k) = The utility function of a type k worker is u(w, e; k) = w-c(e; k). k (a) Does a worker's education level affect productivity? If there was perfect information, what would be the optimal e, w be?
Suppose there are two types of workers, k = G, B, differentiated by their productivity levels. Type G workers have productivity k = 2 and type B workers have productivity k= 1. The cost of achieving a given level of education is higher for type B than type G е workers. The cost function of a type k to achieve education level e is c(e; k) = The utility function of a type k worker is u(w, e; k) = w-c(e; k). k (a) Does a worker's education level affect productivity? If there was perfect information, what would be the optimal e, w be?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Answer with the theoretical content of advanced microeconomics.such as ：1. Hidden information: Adverse selection, screening, insurance markets, credit
rationing.
2. Signalling: Spence model, intuitive criterion, capital structure, cheap talk.
3. Hidden information: Moral hazard and contracting, credit rationing.
4. Institutional Design: Optimal income tax, auctions, contracting.
5. Voting, Gibbard-Satterthwaite Theorem, VCG mechanism.
6. Theory of social choice.
Transcribed Image Text:3. Suppose there are two types of workers, k = G, B, differentiated by their productivity
levels. Type G workers have productivity k = 2 and type B workers have productivity
k = 1. The cost of achieving a given level of education is higher for type B than type G
workers. The cost function of a type k to achieve education level e is c(e; k) =
The
utility function of a type k worker is u(w, e; k) = w- c(e; k).
e
(a)
Does a worker's education level affect productivity? If there was perfect
information, what would be the optimal e, w be?
(b)
Now suppose there is asymmetric information and the productivity level
is known only to the worker. The type of the worker is not observable, but the level
of education is. The firm believes that a worker with higher level of education than
a threshold has higher productivity. Thus, it pays w(e) = 2 if e > eº and w(e) = 1
if e< e. Given this, what will be the level of education that each type will choose
in equilibrium. Find the necessary condition on e for the education level to be an
effective signal of productivity.
(c Discuss the properties of the beliefs of the firm that support this equilib-
rium.
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